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Math Help - Proving conjectures

  1. #1
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    Post Proving conjectures

    Greetings,

    I need some help proving several questions. I got really stuck at these and don't know where to begin. Other than that, these type of questions seem to come out often in my tests so I really need some help. Here we go;

    1. n is a prime => n^2 + n + 1

    2. The interior angle of a regular polygon with n sides is (2n-4)/n right angles.

    3. Given that p and q are odd numbers p^2 + q^2 cannot be divisible by 4.

    Thanks in advance. Explanation of steps would be nice but i can learn from step by step solution if needed.
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  2. #2
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    1. What do you mean? for n=2,3 and 5 n^2+n+1 is prime but for n=7 it isn't.

    2. See Math Online Tutoring, Geometry Online Tutoring

    3. You know p mod 4 = 1 or 3 and q mod 4 = 1 or 3, so that p^2 mod 4 = q^2 mod 4 = 1 and q^2+p^2 mod 4 =2.
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  3. #3
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by Kebex View Post
    Greetings,

    I need some help proving several questions. I got really stuck at these and don't know where to begin. Other than that, these type of questions seem to come out often in my tests so I really need some help. Here we go;

    1. n is a prime => n^2 + n + 1

    2. The interior angle of a regular polygon with n sides is (2n-4)/n right angles.

    3. Given that p and q are odd numbers p^2 + q^2 cannot be divisible by 4.

    Thanks in advance. Explanation of steps would be nice but i can learn from step by step solution if needed.
    1 doesn't make sense to me.. what about n^2 + n + 1?

    ok, for number 3.. any odd number can be represented by 2k + 1 where k is an integer.. so squaring it will give you 4k^2 + 4k + 1.. so what happens when you add the squares of two odd number? you can do it..

    for number two.. you shall observe that the measure of an interior angle of a regular n-gon is given by (180 degrees)(n-2)/n.. but 180 degrees is equivalent to 2 right angles.. and there you go, your desired conclusion follows..

    PS. sorry, i usually don't give a complete solution.. it would be better if the student would understand the process by himself and be able to finish the solution that has been started.. i firmly believe that you will be able to do it..
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